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Optimizing Prime Number Mapping for a Limited Range
Identifying prime numbers within a given range is a fundamental mathematical problem. The ultimate goal is to devise an algorithm that minimizes memory consumption while efficiently identifying primes for numbers up to a specified limit N.
Existing Approach: Bitmasking Odd Numbers
One approach for odd numbers is to use bitmasking, where each bit represents the prime status of a corresponding number. For example, the range (1, 10] would be represented as 1110, where the 1s indicate primes (3, 5, 7, 9).
Refining the Bitmask
However, this approach can be improved by eliminating multiples of five. For the given range, the revised bitmask becomes 11100. However, numbers ending in 1, 3, 7, or 9 still require individual bits.
Optimal Solution
The most compact algorithm for this specific problem varies depending on the range and available computational resources.
<code class="python">def isprime(n): if n == 2: return True if n == 3: return True if n % 2 == 0: return False if n % 3 == 0: return False i = 5 w = 2 while i * i <= n: if n % i == 0: return False i += w w = 6 - w return True</code>
Additional Optimizations
The specific optimization strategy depends on the desired performance and memory constraints for the particular range of numbers being considered.
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